Craving for Chicken: A Probability Adventure!
a) What is the probability that you have to visit four restaurants to find the first one that has chicken?
Are you ready to explore the whimsical world of chicken probabilities?
b) What is the probability that you have to try more than two restaurants?
How likely are you to embark on a chicken escapade to satisfy your cravings?
c) What is the expected number of restaurants that you must visit? The variance?
How many restaurants must you conquer in your quest for the elusive chicken?
Final Answer:
The probability of having to visit four restaurants to find the first one that has chicken is approximately 0.0957. The probability of having to try more than two restaurants is approximately 0.1206. The expected number of restaurants that must be visited is approximately 1.36, and the variance is approximately 0.3264.
Probability of Visiting Four Restaurants
To find the probability of having to visit four restaurants to find the first one that has chicken, we need to consider the probability of each restaurant not having chicken. Since the manager informed you that 82% of restaurants have no chicken, the probability of a restaurant not having chicken is 0.82.
Assuming each restaurant is independent of each other, the probability of having to visit four restaurants to find the first one that has chicken is:
Probability = 0.82 * 0.82 * 0.82 * 0.18 = 0.0957 (rounded to four decimal places)
Probability of Trying More Than Two Restaurants
To find the probability of having to try more than two restaurants, we need to consider the probability of each restaurant not having chicken. Since the manager informed you that 82% of restaurants have no chicken, the probability of a restaurant not having chicken is 0.82. Assuming each restaurant is independent of each other, the probability of trying more than two restaurants is:
Probability = 0.82 * 0.82 * 0.18 = 0.1206 (rounded to four decimal places)
Expected Number of Restaurants Visited and Variance
The expected number of restaurants visited can be calculated by multiplying the probability of visiting each restaurant by the number of restaurants visited. In this case, the probability of visiting a restaurant without chicken is 0.82, and the probability of visiting a restaurant with chicken is 0.18.
Expected Number of Restaurants Visited = (0.82 * 1) + (0.18 * 2) = 1.36 (rounded to two decimal places)
The variance can be calculated using the formula:
Variance = (0.82 * (1 - 1.36)^2) + (0.18 * (2 - 1.36)^2) = 0.3264 (rounded to four decimal places)